Subgroups — C₁₃₇×#33866 #46883252

Order 35072.

548 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3338×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#2241×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#2236×C₁₃₇	C₂	1	2	yes	maximal, complemented
5	#2227×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#2216×C₁₃₇	C₂	1	2	yes	maximal, complemented
7	#2209×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#2188×C₁₃₇	C₂	1	2	yes	maximal, complemented
9	C₄×Q₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
11	C₂×#358×C₁₃₇	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₁₃₇	C₂²	1	2	yes	—
13	#554×C₁₃₇	—	2	1	no	—
14	D₄×Q₈×C₁₃₇	—	2	1	no	—
15	C₂×Q₃₂×C₁₃₇	C₂²	1	1	yes	characteristic
16	C₂×Q₃₂×C₁₃₇	C₂²	1	2	yes	—
17	C₂²×C₁₆×C₁₃₇	C₂²	1	2	yes	—
18	#500×C₁₃₇	C₂²	1	1	yes	characteristic
19	#494×C₁₃₇	C₂²	1	1	yes	characteristic
20	#484×C₁₃₇	—	2	2	no	—
21	#477×C₁₃₇	—	2	1	no	—
22	#467×C₁₃₇	C₂²	1	2	yes	—
23	#467×C₁₃₇	C₂²	1	2	yes	—
24	#462×C₁₃₇	—	2	1	no	—
25	#451×C₁₃₇	—	2	2	no	—
26	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
27	C₄×Q₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×#107×C₁₃₇	C₂²	1	2	yes	—
30	#366×C₁₃₇	C₂²	1	1	yes	characteristic
31	#366×C₁₃₇	C₂²	1	2	yes	—
32	C₄⋊C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
33	#358×C₁₃₇	C₂²	1	1	yes	characteristic
34	#358×C₁₃₇	C₂²	1	2	yes	—
35	#358×C₁₃₇	C₂²	1	2	yes	—
36	#358×C₁₃₇	C₂²	1	2	yes	—
37	#358×C₁₃₇	C₂²	1	1	yes	characteristic
38	#358×C₁₃₇	C₂²	1	2	yes	—
39	C₂²⋊C₁₆×C₁₃₇	C₂²	1	2	yes	—
40	C₄×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃₇	—	2	2	no	—
42	C₂×Q₁₆×C₁₃₇	—	2	4	no	—
43	C₂×Q₁₆×C₁₃₇	—	2	2	no	—
44	C₂×Q₁₆×C₁₃₇	—	2	1	no	—
45	C₂×Q₁₆×C₁₃₇	—	4	2	no	—
46	C₂×Q₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₁₃₇	C₂³	1	2	yes	—
48	C₂×Q₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₇	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₇	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₇	—	4	1	no	—
53	#125×C₁₃₇	—	4	1	no	—
54	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
55	C₂²⋊Q₈×C₁₃₇	—	2	2	no	—
56	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
57	C₂²⋊Q₈×C₁₃₇	—	4	2	no	—
58	C₄×Q₈×C₁₃₇	—	2	1	no	—
59	C₄×Q₈×C₁₃₇	—	2	1	no	—
60	C₄×D₄×C₁₃₇	—	4	1	no	—
61	C₄×D₄×C₁₃₇	—	4	1	no	—
62	C₄×D₄×C₁₃₇	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₇	—	2	2	no	—
64	Q₃₂×C₁₃₇	—	2	2	no	—
65	Q₃₂×C₁₃₇	—	4	2	no	—
66	C₂×C₁₆×C₁₃₇	—	4	2	no	—
67	C₂×C₁₆×C₁₃₇	C₂³	1	2	yes	—
68	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
69	C₂×C₁₆×C₁₃₇	C₂³	1	1	yes	characteristic
70	#107×C₁₃₇	—	2	2	no	—
71	#107×C₁₃₇	—	2	1	no	—
72	#107×C₁₃₇	C₂³	1	1	yes	characteristic
73	#107×C₁₃₇	C₂³	1	1	yes	characteristic
74	#107×C₁₃₇	C₂³	1	2	yes	—
75	C₄⋊C₈×C₁₃₇	D₄	1	1	yes	characteristic
76	#103×C₁₃₇	—	2	1	no	—
77	#103×C₁₃₇	—	2	1	no	—
78	#103×C₁₃₇	—	2	2	no	—
79	#103×C₁₃₇	—	2	2	no	—
80	C₂²⋊C₈×C₁₃₇	D₄	1	2	yes	—
81	C₄×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
82	C₂×Q₈×C₁₃₇	—	2	1	no	—
83	C₂×Q₈×C₁₃₇	—	2	1	no	—
84	C₂×Q₈×C₁₃₇	—	2	2	no	—
85	C₂×Q₈×C₁₃₇	—	4	4	no	—
86	C₂×Q₈×C₁₃₇	—	4	2	no	—
87	C₂×Q₈×C₁₃₇	—	4	1	no	—
88	C₂×Q₈×C₁₃₇	—	8	2	no	—
89	C₂×D₄×C₁₃₇	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₃₇	—	4	2	no	—
91	C₂²×C₄×C₁₃₇	—	4	2	no	—
92	C₂²×C₄×C₁₃₇	C₂×D₄	1	2	yes	—
93	Q₁₆×C₁₃₇	—	2	1	no	—
94	Q₁₆×C₁₃₇	—	2	2	no	—
95	Q₁₆×C₁₃₇	—	2	1	no	—
96	Q₁₆×C₁₃₇	—	2	1	no	—
97	Q₁₆×C₁₃₇	—	2	2	no	—
98	Q₁₆×C₁₃₇	—	4	4	no	—
99	Q₁₆×C₁₃₇	—	8	1	no	—
100	Q₁₆×C₁₃₇	#41	1	2	yes	—
101	C₂×C₈×C₁₃₇	—	2	2	no	—
102	C₂×C₈×C₁₃₇	—	2	2	no	—
103	C₂×C₈×C₁₃₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃₇	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₁₃₇	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₁₃₇	—	2	1	no	—
107	C₄⋊C₄×C₁₃₇	—	2	1	no	—
108	C₄⋊C₄×C₁₃₇	—	2	2	no	—
109	C₄⋊C₄×C₁₃₇	—	4	2	no	—
110	C₄⋊C₄×C₁₃₇	—	4	1	no	—
111	C₄⋊C₄×C₁₃₇	—	4	1	no	—
112	C₄⋊C₄×C₁₃₇	—	4	1	no	—
113	C₄⋊C₄×C₁₃₇	—	4	1	no	—
114	C₄⋊C₄×C₁₃₇	—	4	2	no	—
115	C₄⋊C₄×C₁₃₇	—	4	2	no	—
116	C₄⋊C₄×C₁₃₇	—	4	1	no	—
117	C₄⋊C₄×C₁₃₇	D₈	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
119	C₂²⋊C₄×C₁₃₇	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₇	D₈	1	2	yes	—
121	C₄²×C₁₃₇	—	4	1	no	—
122	C₄²×C₁₃₇	—	4	1	no	—
123	C₄²×C₁₃₇	C₂×D₄	1	1	yes	characteristic
124	C₁₆×C₁₃₇	—	2	1	no	—
125	C₁₆×C₁₃₇	—	2	1	no	—
126	C₁₆×C₁₃₇	—	2	2	no	—
127	C₂³×C₁₃₇	C₂×D₈	1	2	yes	—
128	Q₈×C₁₃₇	—	2	2	no	—
129	Q₈×C₁₃₇	—	4	1	no	—
130	Q₈×C₁₃₇	—	4	2	no	—
131	Q₈×C₁₃₇	—	4	1	no	—
132	Q₈×C₁₃₇	—	4	2	no	—
133	Q₈×C₁₃₇	—	4	1	no	—
134	Q₈×C₁₃₇	—	8	4	no	—
135	Q₈×C₁₃₇	—	16	1	no	—
136	D₄×C₁₃₇	Q₃₂	1	4	yes	complemented
137	C₂×C₄×C₁₃₇	—	2	2	no	—
138	C₂×C₄×C₁₃₇	—	2	2	no	—
139	C₂×C₄×C₁₃₇	—	4	1	no	—
140	C₂×C₄×C₁₃₇	—	4	1	no	—
141	C₂×C₄×C₁₃₇	—	4	1	no	—
142	C₂×C₄×C₁₃₇	—	4	1	no	—
143	C₂×C₄×C₁₃₇	—	4	2	no	—
144	C₂×C₄×C₁₃₇	—	4	2	no	—
145	C₂×C₄×C₁₃₇	—	8	4	no	—
146	C₂×C₄×C₁₃₇	—	16	2	no	—
147	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₇	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₁₃₇	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃₇	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₁₃₇	—	2	2	no	—
152	C₈×C₁₃₇	—	2	1	no	—
153	C₈×C₁₃₇	C₂×#41	1	1	yes	characteristic
154	C₈×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂²×C₁₃₇	—	2	2	no	—
156	C₂²×C₁₃₇	—	2	2	no	—
157	C₂²×C₁₃₇	C₂×Q₃₂	1	4	yes	—
158	C₂²×C₁₃₇	C₂²×D₈	1	1	yes	characteristic
159	C₄×C₁₃₇	—	2	1	no	—
160	C₄×C₁₃₇	—	2	2	no	—
161	C₄×C₁₃₇	—	4	2	no	—
162	C₄×C₁₃₇	—	8	1	no	—
163	C₄×C₁₃₇	—	8	1	no	—
164	C₄×C₁₃₇	—	8	2	no	—
165	C₄×C₁₃₇	—	8	2	no	—
166	C₄×C₁₃₇	—	8	1	no	—
167	C₄×C₁₃₇	C₂×Q₃₂	1	2	yes	—
168	C₄×C₁₃₇	#546	1	1	yes	characteristic
169	C₄×C₁₃₇	#577	1	1	yes	characteristic
170	C₂×C₁₃₇	—	2	4	no	—
171	C₂×C₁₃₇	#3294	1	1	yes	characteristic
172	C₂×C₁₃₇	C₂²×Q₃₂	1	1	yes	characteristic
173	C₂×C₁₃₇	#3416	1	1	yes	characteristic
174	#33866	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₁₃₇	#33866	1	1	yes	characteristic, direct product factor, Sylow
176	#3338	C₂×C₁₃₇	1	1	yes	characteristic
177	D₄×Q₁₆	C₂×C₁₃₇	1	1	yes	characteristic
178	#2241	C₂×C₁₃₇	1	1	yes	characteristic, complemented
179	#2236	C₂×C₁₃₇	1	2	yes	complemented
180	#2227	C₂×C₁₃₇	1	1	yes	characteristic, complemented
181	#2216	C₂×C₁₃₇	1	2	yes	complemented
182	#2209	C₂×C₁₃₇	1	1	yes	characteristic, complemented
183	#2188	C₂×C₁₃₇	1	2	yes	complemented
184	C₄×Q₃₂	C₂×C₁₃₇	1	1	yes	characteristic, complemented
185	D₄×C₁₆	C₂×C₁₃₇	1	1	yes	characteristic
186	C₂×#358	C₂×C₁₃₇	1	2	yes	complemented
187	C₂²×Q₁₆	C₂²×C₁₃₇	1	2	yes	—
188	#554	—	2	1	no	—
189	D₄×Q₈	—	2	1	no	—
190	C₂×Q₃₂	C₂²×C₁₃₇	1	1	yes	characteristic
191	C₂×Q₃₂	C₂²×C₁₃₇	1	2	yes	—
192	C₂²×C₁₆	C₂²×C₁₃₇	1	2	yes	—
193	#500	C₂²×C₁₃₇	1	1	yes	characteristic
194	#494	C₂²×C₁₃₇	1	1	yes	characteristic
195	#484	—	2	2	no	—
196	#477	—	2	1	no	—
197	#467	C₂²×C₁₃₇	1	2	yes	—
198	#467	C₂²×C₁₃₇	1	2	yes	—
199	#462	—	2	1	no	—
200	#451	—	2	2	no	—
201	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
202	C₄×Q₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
203	C₈×D₄	C₂²×C₁₃₇	1	1	yes	characteristic
204	C₂×#107	C₂²×C₁₃₇	1	2	yes	—
205	#366	C₂²×C₁₃₇	1	1	yes	characteristic
206	#366	C₂²×C₁₃₇	1	2	yes	—
207	C₄⋊C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
208	#358	C₂²×C₁₃₇	1	1	yes	characteristic
209	#358	C₂²×C₁₃₇	1	2	yes	—
210	#358	C₂²×C₁₃₇	1	2	yes	—
211	#358	C₂²×C₁₃₇	1	2	yes	—
212	#358	C₂²×C₁₃₇	1	1	yes	characteristic
213	#358	C₂²×C₁₃₇	1	2	yes	—
214	C₂²⋊C₁₆	C₂²×C₁₃₇	1	2	yes	—
215	C₄×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
216	C₂²×Q₈	—	2	2	no	—
217	C₂×Q₁₆	—	2	4	no	—
218	C₂×Q₁₆	—	2	2	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	4	2	no	—
221	C₂×Q₁₆	C₂³×C₁₃₇	1	2	yes	—
222	C₂×Q₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₁₃₇	1	2	yes	—
225	C₄⋊Q₈	—	2	1	no	—
226	C₄⋊Q₈	—	2	1	no	—
227	C₄⋊Q₈	—	4	1	no	—
228	#125	—	4	1	no	—
229	C₂²⋊Q₈	—	2	2	no	—
230	C₂²⋊Q₈	—	2	2	no	—
231	C₂²⋊Q₈	—	4	2	no	—
232	C₂²⋊Q₈	—	4	2	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×D₄	—	4	1	no	—
236	C₄×D₄	—	4	1	no	—
237	C₄×D₄	D₄×C₁₃₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	—	2	2	no	—
239	Q₃₂	—	2	2	no	—
240	Q₃₂	—	4	2	no	—
241	C₂×C₁₆	—	4	2	no	—
242	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
243	C₂×C₁₆	C₂³×C₁₃₇	1	1	yes	characteristic
244	C₂×C₁₆	C₂³×C₁₃₇	1	2	yes	—
245	#107	—	2	2	no	—
246	#107	—	2	1	no	—
247	#107	C₂³×C₁₃₇	1	1	yes	characteristic
248	#107	C₂³×C₁₃₇	1	2	yes	—
249	#107	C₂³×C₁₃₇	1	1	yes	characteristic
250	C₄⋊C₈	D₄×C₁₃₇	1	1	yes	characteristic
251	#103	—	2	1	no	—
252	#103	—	2	1	no	—
253	#103	—	2	2	no	—
254	#103	—	2	2	no	—
255	C₂²⋊C₈	D₄×C₁₃₇	1	2	yes	—
256	C₄×C₈	C₂³×C₁₃₇	1	1	yes	characteristic
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	4	4	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	8	2	no	—
264	C₂×D₄	D₈×C₁₃₇	1	1	yes	characteristic
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	C₂×D₄×C₁₃₇	1	2	yes	—
268	Q₁₆	—	2	1	no	—
269	Q₁₆	—	2	2	no	—
270	Q₁₆	—	2	1	no	—
271	Q₁₆	—	2	1	no	—
272	Q₁₆	—	2	2	no	—
273	Q₁₆	—	4	4	no	—
274	Q₁₆	—	8	1	no	—
275	Q₁₆	#41×C₁₃₇	1	2	yes	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	C₂×D₄×C₁₃₇	1	1	yes	characteristic
279	C₂×C₈	C₂×D₄×C₁₃₇	1	2	yes	—
280	C₂×C₈	C₂⁴×C₁₃₇	1	1	yes	characteristic
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	D₈×C₁₃₇	1	1	yes	characteristic
293	C₂²⋊C₄	—	4	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	D₈×C₁₃₇	1	2	yes	—
296	C₄²	—	4	1	no	—
297	C₄²	—	4	1	no	—
298	C₄²	C₂×D₄×C₁₃₇	1	1	yes	characteristic
299	C₁₆	—	2	1	no	—
300	C₁₆	—	2	1	no	—
301	C₁₆	—	2	2	no	—
302	C₂³	C₂×D₈×C₁₃₇	1	2	yes	—
303	Q₈	—	2	2	no	—
304	Q₈	—	4	1	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	4	1	no	—
307	Q₈	—	4	2	no	—
308	Q₈	—	4	1	no	—
309	Q₈	—	8	4	no	—
310	Q₈	—	16	1	no	—
311	D₄	Q₃₂×C₁₃₇	1	4	yes	complemented
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	8	4	no	—
321	C₂×C₄	—	16	2	no	—
322	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
323	C₂×C₄	C₂×D₈×C₁₃₇	1	2	yes	—
324	C₂×C₄	C₂×D₈×C₁₃₇	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₄×C₁₃₇	1	1	yes	characteristic
326	C₈	—	2	2	no	—
327	C₈	—	2	1	no	—
328	C₈	C₂×#41×C₁₃₇	1	1	yes	characteristic
329	C₈	H(5,𝔽₂)×C₁₃₇	1	1	yes	characteristic
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	C₂×Q₃₂×C₁₃₇	1	4	yes	—
333	C₂²	C₂²×D₈×C₁₃₇	1	1	yes	characteristic
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	4	2	no	—
337	C₄	—	8	2	no	—
338	C₄	—	8	1	no	—
339	C₄	—	8	1	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	1	no	—
342	C₄	C₂×Q₃₂×C₁₃₇	1	2	yes	—
343	C₄	#546×C₁₃₇	1	1	yes	characteristic
344	C₄	#577×C₁₃₇	1	1	yes	characteristic
345	C₂	—	2	4	no	—
346	C₂	#3294×C₁₃₇	1	1	yes	characteristic
347	C₂	C₂²×Q₃₂×C₁₃₇	1	1	yes	characteristic
348	C₂	#3416×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₇
prime radical	C₂×D₄×C₁₃₇	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄×D₄×C₁₃₇ ◁ C₈×D₄×C₁₃₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #2241×C₁₃₇	C₂	semidirect
4. #2236×C₁₃₇	C₂	semidirect
5. #2227×C₁₃₇	C₂	semidirect
6. #2216×C₁₃₇	C₂	semidirect
7. #2209×C₁₃₇	C₂	semidirect
8. #2188×C₁₃₇	C₂	semidirect
9. C₄×Q₃₂×C₁₃₇	C₂	semidirect
11. C₂×#358×C₁₃₇	C₂	semidirect
136. D₄×C₁₃₇	Q₃₂	semidirect
174. #33866	C₁₃₇	direct (N × H)
175. C₁₃₇	#33866	direct (N × H)
178. #2241	C₂×C₁₃₇	semidirect
179. #2236	C₂×C₁₃₇	semidirect
180. #2227	C₂×C₁₃₇	semidirect
181. #2216	C₂×C₁₃₇	semidirect
182. #2209	C₂×C₁₃₇	semidirect
183. #2188	C₂×C₁₃₇	semidirect
184. C₄×Q₃₂	C₂×C₁₃₇	semidirect
186. C₂×#358	C₂×C₁₃₇	semidirect
311. D₄	Q₃₂×C₁₃₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#3338×C₁₃₇	2
D₄×Q₁₆×C₁₃₇	2
#2241×C₁₃₇	2
#2236×C₁₃₇	2
#2227×C₁₃₇	2
#2216×C₁₃₇	2
#2209×C₁₃₇	2
#2188×C₁₃₇	2
C₄×Q₃₂×C₁₃₇	2
D₄×C₁₆×C₁₃₇	2
C₂×#358×C₁₃₇	2
#33866	137

Subgroups — C137×#33866 #46883252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₇×#33866 #46883252